Question

The velocity of water waves (v) may depend on their
wavelength λ, the density of water r and the acceleration
due to gravity, g. The method of dimensions gives the
relation between these quantities is
(a) v (b) v² α g λ
(c) v² α g λ² (d) v² α g⁻¹ λ²

Answer 1

Answer:

Dimension of acceleration due to gravity g is LT

−2

Dimension of Density of water ρ is ML

−3

Let v∝λ

a

g

b

ρ

c

Using Dimensional method:

a+b−3c=1 ( Length )

c=0 ( Mass )

−2b=−1 ( Time )

b=0.5

Hence, a=0.5

∴v∝

gλ

v

2

∝gλ